The San Francisco broker, William Hobi, was so excited to have Mr. Gates as a client that he put a vanity license plate on his Porsche for a few years with the letters MSFT, the trading symbol for the company's stock.

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Times may have changed, but technology billionaires still set the engines racing among Silicon Valley brokers. Social media I.P.O.s, including LinkedIn, Facebook and Twitter, and acquisitions like Facebook's planned $18 billion purchase of WhatsApp have created more than a dozen billionaires, by one count of Forbes magazine data.

Competition to handle their money is intense. "Every day I get a connection request from a wealth manager on LinkedIn," said Michael Cagney, the founder and chief executive of Social Finance, or SoFi, an online student-loan platform in San Francisco that might go public in the next year or two. Mr. Cagney sold another financial software company, Finaplex, in 2007 and runs a hedge fund.

The wealth management dollars up for grabs were detailed last fall at the trial of Mark Cuban, the Dallas billionaire who was acquitted of civil insider trading charges. The first defense witness, Charles McKinney, a former Goldman broker now at Credit Suisse, testified that Mr. Cuban's $695 million account produced annual fees for his firm of about $2.8 million.

Many wealth advisers charge up to 1 percent for the first $5 million or $10 million, reducing the fee in stages to 0.5 percent or lower, subject to negotiation, for amounts exceeding $100 million. Clients with simple portfolios of stocks and bonds may pay less than those in more exotic assets, such as hedge funds or private equity.

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The business prospects are irresistible to brokers as far away as Park Avenue in Manhattan. "You'd be crazy to ignore the wealth being created by the young tech group," said Thorne Perkin, president of Papamarkou Wellner Asset Management, a buttoned-down wealth adviser on Park and 54th Street whose San Francisco clients include Getty family members and Google employees worth hundreds of millions. "It's an incredible opportunity for any money manager."

Of course Goldman and its archrival, Morgan Stanley, the longtime leader of tech I.P.O.s, have the biggest share of the market partly because their brokers can forge close ties with technology titans in the I.P.O. process. Goldman's clients have included Meg Whitman, the chief executive of Hewlett-Packard who was chief of eBay when Goldman led its I.P.O. in 1998. Morgan Stanley's roster has included the venture capital investor Brook Byers and Raymond J. Lane, the former executive chairman of HP.

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But more than two years ago, the charismatic South Africa-born broker Divesh Makan, who had worked at Goldman and Morgan Stanley, took a bite out of their books by starting his own firm, Iconiq Capital, with a pack of Silicon Valley billionaires led by Mark Zuckerberg and Sheryl Sandberg of Facebook and Reid Hoffman of LinkedIn. Iconiq now manages $7.6 billion, up more than 50 percent in the last year.

Mr. Makan has enlisted the aid of Addepar, a start-up backed by an early Facebook investor, Peter Thiel, which adds custom big-data analytics to client reports. He has also put clients into an array of pre-I.P.O. technology start-ups, including the Alibaba Group, the China e-commerce giant that has filed to go public. The posted price for his service is not cheap. He charges up to 1.5 percent of assets under management annually; but all his clients pay less than half that based on their account sizes.

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Already, Mr. Makan's rivals are looking for possible defections. One Iconiq client, Mark Pincus, co-founder of the social gaming developer Zynga, has shifted some of his assets to a Manhattan firm, Seven Bridges Advisors, led by Laurence W. Cohen, chairman of the investment committee at Brown University. Seven Bridges advises institutions and wealthy individuals with an approach similar to that used by large endowments.

Another client who has pulled some assets from Iconiq is Chris Hughes, the co-founder of Facebook who bought The New Republic in 2012.

Managing money for the ultrawealthy has its own demands and challenges.

For example, it is hard for many successful technology entrepreneurs to accept a conservative investment approach, said Scott Clemons, chief investment strategist in the private banking unit of Brown Brothers Harriman in Lower Manhattan. "For someone who is in the right place at the right time and figures out the right app for the right market, the natural psychology is to think, 'Well, that was easy!' "

Some firms emphasize service, with Iconiq arranging private jets and flight crews as well as tax and estate planning. Harris myCFO will supervise home construction and buy and insure exotic cars as part of its concierge service, said Ron Gong, co-head of its Palo Alto, Calif., office, who recently bought a $105,000 Mercedes station wagon and a $299,000 Ferrari for separate clients.

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Other firms lead with cold cash. Deutsche Bank, for instance, has built its Valley presence based in part on its willingness to undertake complicated financings. Two years ago, a Deutsche private banking team in New York and San Francisco closed a $25 million loan on short notice in a matter of just a few business days, people briefed on the matter said. Deutsche Bank did not disclose the clients' names. People close to the matter said the borrowers were the brothers Cameron and Tyler Winklevoss, whose battle over a stake in Facebook became part of the 2010 movie "The Social Network." Deutsche Bank has since won more of the brothers' business, arranging a $9 million mortgage refinancing in Los Angeles for them last year.

Not everything works out all the time. The net worth of two Goldman clients, Weili Dai and Sehat Sutardja of Los Altos, Calif., the husband-and-wife co-founders of Marvell Technology Group, the maker of mobile phone chips, hit $1.36 billion after the firm led Marvell's I.P.O. in 2000. But they lost $192 million when forced to sell stock bought in part with borrowed money in 2008, the couple said in an arbitration claim filed against the firm. In March, a securities industry panel denied the claim. It is not just the multimillionaire crowd that is attracting attention. An automated investment service, Wealthfront, a venture-backed start-up in Palo Alto that features low-cost index funds, has courted rank-and-file employees at several social media companies including Facebook, Dropbox, Airbnb and Twitter, according to its chairman, Andy Rachleff.

Some technology titans are getting in the investment management game. Mr. Gates has Cascade Investments, led since 1994 by Michael Larson, which manages his money. Google's executive chairman, Eric E. Schmidt, has a family office and a venture investment arm. Amazon.com's chief executive, Jeffrey P. Bezos, has a venture unit called Bezos Expeditions.

Some have even opened their doors to outsiders. MSD Capital, a $15 billion family office started in 1998 by the computer executive Michael Dell has four funds managed by an affiliate, MSDC Management, which also accepts money from other institutions and wealthy individuals.

"They're all chasing the marquee Silicon Valley names," said Larry Albukerk, a San Francisco broker at EB Exchange who arranges stock sales for investors in pre-I.P.O. companies. "It's not just the management fees from a billionaire's account, but also the potential for favorable buzz," he added. "One big name can attract dozens of other clients. It can make their business."